Problem: Simplify the following expression: $ r = \dfrac{4}{5} + \dfrac{t + 7}{-9} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-9}{-9}$ $ \dfrac{4}{5} \times \dfrac{-9}{-9} = \dfrac{-36}{-45} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{t + 7}{-9} \times \dfrac{5}{5} = \dfrac{5t + 35}{-45} $ Therefore $ r = \dfrac{-36}{-45} + \dfrac{5t + 35}{-45} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-36 + 5t + 35}{-45} $ $r = \dfrac{5t - 1}{-45}$ Simplify the expression by dividing the numerator and denominator by -1: $r = \dfrac{-5t + 1}{45}$